Born-Infeld gravity with a Brans-Dicke scalar

Understand

Recently proposed Born-Infeld (BI) theories of gravity assume a constant BI parameter ($\kappa$).

• However, no clear consensus exists on the sign and value of $\kappa$.
• Recalling the Brans-Dicke (BD) approach, where a scalar field was used to generate the gravitational constant $G$, we suggest an extension of Born-Infeld gravity with a similar Brans-Dicke flavor.
• Thus, a new action, with $\kappa$ elevated to a spacetime dependent real scalar field, is proposed.